Question

if both (x-2) and (x-½) are factors of px²+5x+r show that p=r



please answer it correctly wrong answer will be reported​

Answer 1

Answer:

r=-2 , p=-2

therefore p=r

Step-by-step explanation:

so x=2 and x=1/2 are the two roots (another name for factors)

of px2 + 5x + r

substitute x=2 in the equation , we get

4p + 10 + r = 0 ............(1)

substitute x=1/2 in the equation , we get

p/4 + 5/2 + r = 0

taking lcm...............

(p+10+4r)/4 = 0

multiply 4 on both sides we get...

p+10+4r  ...............(2)

you can solve it as linear equation in two variables

4p + 10 + r = 0

(p+10+4r = 0 ) * 4

..................................................

4p+10+r=0 ..................(3)

4p+40+16r=0 ..........................(4)

now subtract

 equations (3) - (4) u get...........

-30-15r=0

r=-2

substitute r= -2 in eq (3)

4p + 10 -2 =0

4p+8=0

p=-2

r=p=-2

Answer 2

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